Quantum-enhanced metrology with network states

TL;DR

This paper establishes fundamental limits on quantum network states for distributed parameter estimation, proving the necessity of genuine multipartite entanglement for quantum advantage and proposing a protocol to reach the Heisenberg limit.

Contribution

It provides a general bound on quantum network states for parameter estimation, introduces an entanglement witness, and designs a probabilistic protocol to achieve the Heisenberg limit.

Findings

Genuine multipartite entanglement is necessary for quantum advantage.

Local network states cannot reach the Heisenberg limit.

A probabilistic protocol can attain the Heisenberg limit while preserving privacy.

Abstract

Armed with quantum correlations, quantum sensors in a network have shown the potential to outclass their classical counterparts in distributed sensing tasks such as clock synchronization and reference frame alignment. On the other hand, this analysis was done for simple and idealized networks, whereas the correlation shared within a practical quantum network, captured by the notion of network states, is much more complex. Here, we prove a general bound that limits the performance of using quantum network states to estimate a global parameter, establishing the necessity of genuine multipartite entanglement for achieving a quantum advantage. The bound can also serve as an entanglement witness in networks and can be generalized to states generated by shallow circuits. Moreover, while our bound prohibits local network states from achieving the Heisenberg limit, we design a probabilistic protocol that, once successful, attains this ultimate limit of quantum metrology and preserves the privacy of involved parties. Our work establishes both the limitation and the possibility of quantum metrology within quantum networks.